An economics professor has devised an interesting game to test the understanding of his students. He randomly selects two students from his class and gives a $50 bill to one of them

He then asks him what percentage of $50 he would give to his classmate. The first student can choose any percentage he wishes, while the second student can choose whether or not to accept the offer. If the second student does not accept the offer, the professor will take the bill back but if he accepts the offer, the money will be divided in the ratio decided by the first student. a) What is the likely outcome of this game if both the students value more money to less? b) What is the likely outcome of this game if the second student values fairness?

a) The first student is likely to offer the lowest possible amount to the second student. This is because the second student will always accept any offer made by the first student if he prefers more money to less. Given that his classmate will always accept his offer, the first student is better off by offering the lowest possible amount.
b) If the second student values fairness, he will not accept an unfair allotment of the money offered by the first student. If an unfair allotment is offered, neither of them will get any money. If the first student knows that the second student prefers fairness, then the first student has an incentive to offer a more equal allotment.